Omar is 3 times as old as Christopher. Ten years ago, Omar was 5 times as old as Christopher. How old is Omar now?
Answer: We can use the given information to write down two equations that describe the ages of Omar and Christopher. Let Omar's current age be $o$ and Christopher's current age be $c$ The information in the first sentence can be expressed in the following equation: $o = 3c$ Ten years ago, Omar was $o - 10$ years old, and Christopher was $c - 10$ years old. The information in the second sentence can be expressed in the following equation: $o - 10 = 5(c - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $o$ , it might be easiest to solve our first equation for $c$ and substitute it into our second equation. Solving our first equation for $c$ , we get: $c = o / 3$ . Substituting this into our second equation, we get: $o - 10 = 5($ $(o / 3)$ $- 10)$ which combines the information about $o$ from both of our original equations. Simplifying the right side of this equation, we get: $o - 10 = \dfrac{5}{3} o - 50$ Solving for $o$ , we get: $\dfrac{2}{3} o = 40$ $o = \dfrac{3}{2} \cdot 40 = 60$.